1. **State the problem:** A motorcycle starts with an initial velocity of $12$ m/s, accelerates at $2.5$ m/s², and travels a distance of $80$ m. We need to find its final velocity. 2. **Formula used:** We use the kinematic equation that relates initial velocity ($v_0$), acceleration ($a$), displacement ($s$), and final velocity ($v$): $$v^2 = v_0^2 + 2as$$ This formula is useful when time is not given. 3. **Substitute the known values:** $$v^2 = (12)^2 + 2 \times 2.5 \times 80$$ 4. **Calculate the right side:** $$v^2 = 144 + 2 \times 2.5 \times 80 = 144 + 400 = 544$$ 5. **Find the final velocity by taking the square root:** $$v = \sqrt{544}$$ 6. **Simplify the square root:** $$v = \sqrt{16 \times 34} = 4\sqrt{34} \approx 23.32 \text{ m/s}$$ **Final answer:** The final velocity of the motorcycle is approximately $23.32$ m/s.